There are two hostels in the Gare du Nord area. Since I always stay in a two star hotel in Nord, I've checked out both of these hostels for possible future stays as I am going to be staying in Nord anyway.
One is St Christophers located between Gare de l'Est and Nord. That is a big hostel. From seeing the guests each time passing there and the outside, I didn't find it to be awful. On hostels these things most of the time don't bother me. This hostel is a private independent one, ie not part of HI. I don't recommend this one if you don't like big hostels. To me it makes no difference.
The other hostel is on the other side of Rue de Dunkerque, Vintage Hostel, located at the boundary of the 9th and 10th districts, en route to Montmarte. Between the two Vintage is better, much nicer location, refurbished, a bit smaller. ca 15 mins walk once exiting Nord by turning right. Vintage is also a private independent hostel I recommend this hostel.
I'm over 40 years your daughter's senior. I stayed exclusively in hostel dorm rooms at her age and earlier and still do not preclude this option for the occasional stay...just all depends on the hostel and its location.